Sentence AXIOM-OF-INFINITY

There is a bounded set containing a set, a set that properly contains that set, a third set that properly contains the second set, and so forth. In short, there is at least one bounded set of infinite cardinality.
Instance-Of: Sentence
Defining-Axiom: 
'(Exists (?U)
         (And (Bounded ?U)
              (Not (Empty ?U))
              (Forall (?X)
                      (=> (Member ?X ?U)
                          (Exists (?Y)
                                  (And (Member ?Y ?U)
                                       (Proper-Subset ?X ?Y)))))))